292 Royal Society. 



In order to estimate the velocity of the currents, one of the ane- 

 mometric discs was placed within a short zinc tube three inches in 

 diameter, the lower end of which was accurately fitted into an aspi- 

 rator capable of containing thirty-six gallons of water. By drawing 

 off in a given time a quantity of water equal in bulk to the cubic 

 contents of one of the tubes described in the former paper, the 

 velocity of a current required to produce a given number of rotations 

 of the disc was determined. 



The experiments were varied by altering the height of water in 

 the aspirator, and thereby changing the velocity, while the exit- 

 orifice remained unaltered. 



By ascertaining the number of rotations of the anemometric disc, 

 caused by currents of air of different velocities thus produced, he 

 was enabled to arrive at a measure of the velocities in tubes placed 

 in a still atmosphere, as described in his former paper. 



The author in that paper pointed out a correspondence between 

 the variations of force in the upward currents of atmospheric air in 

 the tubes and variations in the humidity of the atmosphere, and 

 expressed his belief that the variations were attributable in great 

 measure to the varying hygrometric conditions of the atmosphere. 



In further proof of this position, he has appended two tables, 

 showing that both natural and artificial increase of atmospheric 

 humidity are accompanied by increase in the velocity of the rotations, 

 and that in each case increase of humidity is attended by increase of 

 velocity, independent of temperature. 



"On the StabiUty of Loose Earth." By W. J. Macquorn Ran- 

 kine, Esq., C.E., F.R.SS.L. & E., Regius Professor of Civil Engi- 

 neering and Mechanics in the University of Glasgow. 



The object of this paper is to deduce the mathematical theory of 

 that kind of stability which depends on the mutual friction of the 

 parts of a granular mass devoid of tenacity, from the known laws of 

 friction, unaided by any hypothesis. 



The fundamental principle of the internal stability of such a mass 

 has already been published in the ' Philosophical Magazine ' for De- 

 cember, 1856, viz. that the ratio of the difference to the sum of the 

 greatest and least pressures at each point of the mass must not 

 exceed the sine of the angle of repose. 



The principles of the general theory of the internal equilibrium of 

 a solid mass are expressed in a form suited to the special subject of 

 the paper. For the purpose of determining the conditions of equi- 

 librium under its own weight, of a solid mass whose upper surface is 

 that generated by the motion of a horizontal straight line along a 

 line of any figure described on a vertical plane at right angles to the 

 generating line, the mass is supposed to be divided into layers of 

 equal horizontal thrust by a series of surfaces, which layers are sub- 

 divided into elementary horizontal prisms by vertical planes normal 

 to the vertical plane first mentioned. For independent variables 

 there are taken the horizontal coordinate in this plane, and the total 

 horizontal thrust from the upper surface down to a given surface of 



